ANALYZING INTERORGANIZATIONAL INFORMATION SHARING STRATEGIES IN B2B E-COMMERCE SUPPLY CHAINS

Robert J. Kauffman (contact author)

Carlson School of Management University of Minnesota

rkauffman@csom.umn.edu

Hamid Mohtadi Department of Economics

University of Wisconsin, Milwaukee mohtadi@csd.uwm.edu

Last revised: August 1, 2003

Note: This paper will be presented at the 2003 INFORMS Conference on Information Systems

and Technology, October 2003, Atlanta, GA. ______________________________________________________________________________

ABSTRACT

Information sharing in procurement occurs in many rich and varied industry contexts in which managerial decisions need to be made and organizational strategy needs to be formulated. This paper extends the theoretical results that are available to understand how information sharing ought to work in procurement contexts that involve investments in interorganizational information systems and collaborative planning, forecasting and replenishment practices. Our primary research question is: How and under what circumstances does a firm that plays the role of a buyer in supply chain management decide to share information on key variables, such as point-of-sale consumer demand data with its supplier, up the supply chain? The answers that we provide are based on the analysis of a sequential form game-theoretical model of buyer and supplier profits in the presence of uncertainties about final consumer demand, as well as the different operational cost regimes associated with information sharing and information withholding strategies, and the information technologies that support them. Our results provide normative guidance to supply chain buyers about how to interpret different demand uncertainty scenarios to improve the likelihood that their decisions will maximize the value of their firms.

KEYWORDS: Business-to-business e-commerce, economic analysis, electronic commerce, information sharing, organizational strategy, procurement, supply chain management, theory-building research, uncertainty.

______________________________________________________________________________

ACKNOWLEDGEMENTS. The authors wish to thank Anandhi Bharadwaj, Sri Narisimhan and Radhika Santhanam and two anonymous for their suggestions on improving a prior version of this paper. We also thank Qizhi Dai, Kunsoo Han and Jean Kinsey for their involvement with us in related research on B2B e-commerce, procurement and electronic markets that enriches the theoretical perspective that we offer here.

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INTRODUCTION

Recent increases in computing power have enabled algorithm-based optimization approaches

for firms to manage uncertainties that arise in supply chain management as never before (Aviv,

2001; Kumar, 2001). This has prompted increasing systems and technological integration and

information sharing across firms (Ball et al., 2002), as well as new managerial approaches, such

as Web-based electronic data interchange (EDI), vendor-managed inventory and collaborative

planning, forecasting and replenishment (Aviv and Federgruen, 1998; Seidmann and

Sundararajan, 1997) and new contractual approaches in procurement (Cachon and Lariviere,

1999; Kleindorfer and van Wasselhove, 2003). All these approaches take advantage of the

interdependent aspect of value that interorganizational information sharing can create for

procurement of supplies in the presence of the appropriate business process capabilities (Riggins

and Mukhopadhyay, 1994). Such arrangements create the possibility for different equilibrium

pricing arrangements, and different terms set and agreed upon by buyers and suppliers.

Information sharing in procurement occurs in many rich and varied industry contexts in

which managerial decisions need to be made and organizational strategy needs to be formulated.

The common goals of firms in this context are effective inventory management and cost

minimization when supply disruptions occur. In the former case, it is well known that firms

must protect against the bullwhip effect, in which the effects of demand variability are amplified

across the firms up the value chain (Lee, Padmanabhan and Whang, 1997). Yet, knowledge in

this domain is often the buyer's strategic asset. Buyers benefit from the cross-functional value of

information sharing, improving production planning and creating a basis for the transformation

of marketing and sales strategy (Seidmann and Sundararajan, 1997). However, suppliers may use

such information against buyers, tempering the latter’s desire to adopt IT and risk possibly losing

competitive advantage in procurement (Whang, 1993). The result is that buyers will have a

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diminished incentive to share information due to the risk exposure (Laffont and Tirole, 1999),

while taking appropriate advantage of the strategic of value of their private information (Chen,

1998; Gavirneni, Kapuscinski, and Tayur, 1999).

This paper extends the existing theoretical understanding of information sharing in e-

commerce procurement contexts in supply chains. The paper’s focus is on information strategies

of a buyer firm vis-à-vis its supplier, and thus the buyer’s decision regarding the adoption of

information technology (IT) that involves sharing of information. It models the information

strategies of a buyer in a supply chain and includes the possibility of withholding information

upstream from its supplier because of the potential for supplier opportunism, where it is observed

(Clemons, Reddi and Row, 1993; Seidmann and Sundararajan, 1997; Whang, 1993).

In the circumstances that we consider, we find that such information withholding strategies

actually may yield full information, if the supplier is able to infer buyer’s private information,

but may nonetheless leave the buyer worse off ex post, because of the buyer’s initial avoidance

to invest in the appropriate ITs. This may leave the buyer better off if the supplier’s inference is

incomplete, so that the final equilibrium is informationally inefficient. Should an information

withholding strategy lead to a buyer being unwilling to adopt any IT, we have a classic

application of the “asset hold-up” problem (Schmalensee and Willig, 1989).

In the food industry, Nakayama (2000) shows that information exchange plays a role in the

power relationship between supermarkets and suppliers, impacting their trust and IT adoption

among firms. An instance is when food retailers use EDI for inventory coordination. Suppliers’

knowledge of the buyer’s parameters leads them to monitor and control the buyer’s mark-up

more effectively, reducing their incentive to share point-of-sale (POS) data with suppliers.

This source of incentive for the buyer to withhold information is different from the existing

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understanding of the buyer’s incentives to distort order information when a supply shortage is

anticipated, leading to the familiar bullwhip effect (Lee, Padmanabhan and Whang, 1997) or to

exaggerate the forecast of final demand to induce supply to build larger capacity (Cachon and

Lariviere, 2002). This issue has also been treated by economists in more general terms, related

to inter-firm strategic information sharing in monopolistic, duopolistic, oligopolistic and

competitive settings (e.g., Gal-Or, 1985; Li, 1985 and 1999; Raith, 1996). Other related studies

in Operations Management include Lee, So and Tang (2000) and Gavirneni, Kapuscinski and

Tayur (1999) and Cachon and Fisher (2000). The authors generally focus on the normative issue

of the advantages of information sharing in reducing inventory and increasing supply chain

efficiency, but do not discuss buyer incentives to withhold information. Whang (1993) studies

information sharing from a different perspective, focusing on information “garbling” versus

information sharing strategies of a supplier vis-à-vis its downstream buyer. Our perspective is

different from these, but similar to another one offered by Li (2002). He focuses on information

sharing and withholding strategies within the context of horizontal competition. The incentive of

the buyer to share or withhold information from the supplier is driven by the leakage of

information to potential rivals, rather than by supplier opportunism. We share with Li (2002) the

notion of information inference stemming from the observed actions of the firm. But the

inferring party in our analysis is the supplier, rather than competing buyers.

Another unique aspect of this paper is that the information sharing game that we specify

takes place in an environment of uncertainty in which both the final demand facing the buyer and

procurements that the buyer orders from its supplier are each subject to random shocks that are

independent of each other. Thus our paper differs from a recent paper by Radhakrishnan and

Srinidhi (2003) who consider demand side variability as the main influence; we consider an

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independent procurement side variability due to random errors. For example, Dell reports a

significant degree of statistical error in the procurement process that was reduced by sharing

information with its suppliers: from 200 errors per million orders to just 10 (Perman, 2001).

We next turn to the development of a model that incorporates this consideration and enables

us to understand the dynamics and the strategic considerations regarding IT adoption and

information sharing. Our analysis will be accomplished in one preliminary and two analysis

stages. There is a critical assumption in our work that does not appear in the others: all output

pricing decisions for the firm will have a shorter time horizon than decisions about IT

investments that permit information sharing. In the following section, we discuss some of the

theoretical perspectives that provide a foundation for the analysis perspective and modeling

approach that we will adopt throughout the paper. In the first stage, we develop several

propositions on the impacts of managerial uncertainty relative to procurement. In the second

stage, we analyze buyer-supplier information sharing by modeling the buyer's investment in

information sharing via choices about the appropriate IT platform solutions as an outcome that is

obtained in a sequential game in extensive form between the supplier and the buyer. The results

are developed for three scenarios that capture the final consumer demand uncertainties that

supply chain buyers face. We characterize the results with propositions that guide a managerial

decisionmaker on how to think through the available strategy choices.

MODELING INFORMATION SHARING IN SUPPLY CHAIN MANAGEMENT

Different perspectives have developed in recent research on the appropriateness and

implications of information sharing and the related strategies that firms develop. Lee and Whang

(2000) note the trade-off that buyers in procurement must consider by asking: What is the

minimum set of information to share with my supply chain partners without risking potential

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exploitation? Gal-Or (1985) showed how information sharing can lead to results that may be

socially efficient, creating greater value in the economy, even if they are not optimal from a

specific firm’s point of view. Seidmann and Sundararajan (1998) analyzed how information

sharing by firms along the supply chain can reduce costs and diminish vertical transactional

inefficiencies. There may also be strategic implications, as horizontal information leaks may

occur. Nakayama (2000) studied the strategic value of supply chain information in the food

industry. He learned that buyer-supplier power is a driver of buyers’ willingness to adopt of EDI

technology. Nakayama’s survey (2000) also finds that “there is evidence that power shifts

towards suppliers with EDI links.” Kinsey and Ashman (2000) also have found that insufficient

trust deters retail grocers from sharing critical information with their suppliers.

Other industries have seen similar considerations related to information and knowledge

sharing arise as well. In retail banking, for example, Thakor (1999) has argued that early

adoption of automated teller machines was driven by strategic considerations. Electronic

banking systems adoption involving interorganizational sharing of ATMs was driven by such

strategic considerations (Kauffman, McAndrews and Wang, 2000), as well as by the expected

changes in transactions costs (Clemons and Kleindorfer, 1992).

In many supply chain contexts, the buyer is concerned about building bargaining or market

power in the presence of choice about whether and how to share inventory information with

suppliers. Suppliers tend to have market power relative to the buyer, even though there are cases

(e.g., Dell, Wal-Mart and Target) where the buyer has close to monopoly power over the sellers.

Both the buyer and supplier, however, face final demand uncertainties and procurement errors

between orders and deliveries that they prefer to eliminate. We will focus on cases in which the

supplier possesses market power relative to the buyer so we do not consider monopoly buyers.

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However although the buyer is competitive with respect to the supplier, it is large enough to be

able to exercise market power relative to its own customer base.

Modeling Preliminaries

We consider a competitive retail firm (i.e., the “buyer”) that exerts some price control on its

products (i.e., acts as a price setter), but faces critical demand uncertainties. Buyer supplies are

procured in a competitive market subject to supply uncertainties from the supplier, stemming

from its own unavailability of goods, either due to inappropriate forecasting or production

disruption or delays in delivery. The critical aspect is in the extent to which the buyer and the

supplier face the possibility of procurement errors due to mismatched orders and deliveries, in

terms of timing delay, incorrect specifications of the goods ordered, or incorrect quantities.

Stochastic Demand and Supply Uncertainties. Demand uncertainties arise because final

sales are subject to stochastic shocks that managers cannot predict. To represent this, we let

, with δ ∼ f(0,σsf

dsf

ds qqqqq )1( δδ −=⇒=− δ2) and δ ∈ [-1,1]. qd f is the final level of sales (or

final demand, d f), qs is supply quantity received from wholesale supplier s and δ is management

estimation error (in relative terms) of final demand due to random shocks. The random variable δ

is symmetrically distributed with distribution f, mean 0 and variance σδ2. To ensure that qd f ≥0,

the lower bound on δ must be a truncated symmetric distribution (such as the truncated normal)

in the interval [-1,1]. Supply uncertainties are modeled for a control variable, qo, that represents

quantity to be ordered from a supplier, q osoos ququqq )1( +=⇒=− , with u ∼ g(0,σu2) and u∈ [-

1,1] The distribution g can be any symmetric truncated distribution. Supply fluctuation sources

are likely to be independent of any random demand fluctuations, so cov(δ, u) = 0. Then, the

variable qo is the control variable that management wishes to optimize.

Calculating the Buyer’s Profits. A buyer b’s expected profits, E(πb ), are calculated by

7

integrating its objective function over two uncertainty dimensions, demand and supply, with

πb ( qs, qd f ) intended to represent the profit for a given supply quantity qs and final consumer

demand qd f, prior to the application of the stochastic process operators:

∫ ∫− −

=1

1

1

1

)(),()()( δδππ dfqqduugE fdsrb . (1)

To calculate expected profits, we evaluate the conditional expectation, E(πb(qs)), over qd f:

)qq(prob)qq(s)]qq(probq

)qq(probq[c)qq(prob|q)q(P)qq(prob|q)q(P))q((Ef

dsf

dsf

dss

fdss

fdsqq

fd

fd

fdsqqsssb d

fsd

fs

>−−>⋅+

<⋅−>⋅+<⋅=π>< (2)

In this expression, P( ) is the inverse demand function, c is total unit cost of obtaining product

from distributors, with product procurement cost, cp, and transaction cost, ct, of bringing the

product to market (in terms of documentation, invoicing, advertisement). The supplier firm can

exert market power over cp while ct is internal to the buyer firm. The parameter s denotes unit

costs associated with excess or carry-over inventory and stock. It is intended to make the model

more realistic by allowing for the possibility that the firm must absorb the costs of storing or

disposing of inventory that was ordered in excess of that level necessary to meet final consumer

demand.

We can express Equation 2 in δ by noting 0≤ δ ≤ 1 for qs ≥ qd f and 0< δ ≤− 1 for qs < qd

f,

(3) δδδδδδδδδπ dfqscqdfqqPdfqqPqE sssssssb )()()1()]1([()()())((1

0

1

0

0

1∫∫∫ −−−⋅−+=

−

This can be simplified because qs is a given at this stage, and P(qs)qs is independent of δ . Since

f(δ) is symmetric in δ, and the integral covers half the range of δ, the first integral can be

evaluated as [P(qs)qs]/2 . We define the final term, the demand error integral, Ωδ, as,

, so the buyer’s conditional profit expectation is: δδδδ ∫≡Ω1

0

)( df

8

. (4) δδδδδπ Ω−−−⋅−+= ∫ sssssssb sqcqdfqqPqqPqE1

0

)()1()]1([()()2/1())((

Unanticipated Over-Supply. Ωδ represents the mean value of δ, the extent that actual

demand falls short of supply, i.e., δ > 0. So Ωδ indicates the extent to which there is, on

average, unanticipated over-supply or inventory build-up. Also, from δ ∈ (0,1), it follows that

Ωδ < 1. The unconditional value of expected profits is found by integrating the conditional

expectation over the supply variance, u, to yield:

. (5) duugqEE sbb )())(()(1

1

ππ ∫−

=

We can obtain an explicit form of E(πb (qs)), which will involve stochastic parameters, δ and

u, as arguments of the inverse demand function P[qo(1+u)] and P[qo(1+u)(1-δ)]. Using Taylor

series approximation of inverse demand around the non-stochastic order size, qo, and integrating

the results over the appropriate density functions, the buyer’s expected profit becomes:

),,()(')()()1()( 222δσδ σσπ Ω+Ω+−Ω−≅ uooodoob AqPqqscqqPE . (6)

In this expression, the final term, A( ), involves the variance of the demand error integral and is

δδδδδδ σσσσσσ Ω−++Ω−≡Ω )()21(),,( 2222122

uuuA . Finding optimum orders qo* requires

the concavity of expected profits, E(πb). This imposes a limit on unanticipated overstock size,

Ωδ , so that )2

1(210)( 2

2

2δ

δσπ

+<Ω⇒<o

b

dqEd .

The Buyer’s Optimizing Behavior in the Presence of Linear Demand

We begin with a brief analysis of the buyer’s order level selection, qo, to maximize expected

profits. We examine the case of linear demand, with P(qo) = a - zqo,. This demand structure

supports a tractable illustrative analysis. The first order condition for optimization yields:

9

)21)(1(

)()(21*0)(

2212

δδ

δ

Ω−σ+σ+Ω+−−

⋅=⇒=π

uo

o

b sacaz

qdq

dE . (7)

From the expression for qo* presented earlier, we know that maximum expected profits are:

)21)(1(])()[(

41*

2212

2

δδ

δ

Ω−σ+σ+

Ω+−−⋅=π

u

eb

sacaz

. (8)

If the buyer firm is to remain viable in the marketplace, its optimum order size and profits

must be positive. Since the denominators of Equations 7 and 8 are positive (by the concavity of

expected profits), the firm is viable if the numerator in Equation 7 is positive, i.e., if

unanticipated overstock has an upper bound, saca

+−

<Ωδ . Thus, Ωδ is limited

by ]),2

1(21min[

2

saca

+−

+ δσ .

In Equations 7 and 8, supply and demand uncertainties, σ2δ and σ2

υ , affect expected output

and profits adversely, as would be expected, 0,2

*

2

*

<∂

∂

∂

∂

u

er

er

σ

π

σ

π

δ

and 0,2

*

2

*

<∂

∂

∂

∂

u

eo

eo qq

σσ δ

. However, the

effect of the unanticipated over-supply parameter, Ωδ, is mixed, exerting opposite influences via

the numerator and the denominator of Equations 7 and 8. The origin of this is found in the

expression for expected profits, Equation 6: Ωδ affects expected profits adversely via the

revenues and inventory costs, which are the first two terms in the expression. But it also

positively affects expected profits through the slope of inverse demand P'(qo), which is negative.

This is tied to the market power of the buyer. For a competitive buyer P'(qo) = 0 and

unanticipated oversupply, Ωδ , reduces expected profits unambiguously. However, buyers with

some market power are in a position to reduce the price level to respond to excess inventory

build-up when supply exceeds sales (i.e., qs > qd f , or δ >0), moderating the adverse effect of

overestimating the demand. This leads us to assert:

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Proposition #1 (The Market Power Proposition): Buyer firms that have greater market power with respect to their final consumers are better able to absorb adverse effect of oversupply shocks by reducing prices than those with little or no market power.

The overall net effect of inventory overstock is negative, 0,**

<Ω∂

∂Ω∂

∂

δδ

π oe

r q , if Ωδ has an upper

bound, saca

u+−

−+< 2

211 σδΩ .

The Supplier’s Optimizing Behavior Relative to the Buyer

We next analyze the optimizing behavior of the supplier relative to the buyer. To do this, we

first decompose the unit cost into its components, the procurement cost and the transaction

cost, , as in the context of our calculation of the buyer’s profits. We assume that the

seller possesses market power and acts monopolistically with respect to the buyer. This is

reflected in the supplier’s ability to influence the procurement costs, c

tp ccc +=

p , that it charges the buyer.

The supplier’s resulting profits are given by:

))(()()( cqEvcE sps −=π (9)

where v is the unit cost of production, and )()1( cquq os += captures uncertainty in the source of

supply. The function qo(c) = )2

)(2

21

δδ

δ

Ω−σ+1)(1()(

21

2σ+Ω+− sa is determined by Equation 7. Thus,

Equation 9 shows a Stackelberg supplier that acts as a “leader,” observing the buyer's downward

sloping demand, as a function of the unit cost of procurement, c. Substituting from

into Equation 9, the supplier's expected profits become: )()1( cquq os +=

−⋅

u

caz

(10) )()()()1).(()()(1

1tpoptpops ccqvcduuguccqvcE +−=++−= ∫

−

π

Obviously, the effect of product costs charged by the supplier is positive on supplier profits

to the extent they can be passed on to the buyer, due to cp - v in Equation 10. But we also know

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from the expression,saca

+−

<Ωδ , that this effect is negative to the extent that it can trigger an

adverse demand response on the part of the buyer firm via qo (cp + ct). Substituting for qo(c)

from Equation 8 and remembering that c = cp+ ct, balancing these effects means that the supplier

charges the buyer:

])([21*0

)(vsacac

dcdE

tpp

s +Ω+−−⋅=⇒= δπ

(11)

Notice that an increase in Ωδ via 0<Ω∂

∂

δ

*c p reduces the optimum charge by the wholesaler to the

buyer. This leads to our second proposition:

Proposition 2 (The Procurement Cost-Overstock Link Proposition): The procurement cost that the supplier firm charges its downstream client firm is inversely related to the size of the overstock facing the buyer firm.

Substituting from Equations 8 and 11 into Equation 10 yields an expression for the supplier’s

maximum expected profits (analogous to what we computed for the buyer):

]2

211)[1(

)(])[()(.

41

22

222

*

δδ

δ

Ω−σ+σ+

++

+−Ω+−+−

=πu

te

ssa

vssa

vssavca

z (12)

This expression raises a number of key issues that deserve discussion. First, as in the case of

the buyer, supplier profits fall with uncertainty in final demand facing the buyer and the

uncertainty associated with the variance between the supply of goods and buyer's orders, based

on the second derivatives, 0,2

*

2

*

<∂

∂

∂

∂

u

es

es

σ

π

σ

π

δ. Thus, our analysis shows that the buyer and seller

along the supply chain benefit from a reduction in the market variance as well as improved

coordination between orders and deliveries. Second, the effect of unanticipated overstock at the

level of final sales to the consumer is affected different ways: negatively through the numerator

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and positively via the denominator. To gauge the overall effect, we need to consider the

expression for the supplier’s expected profit, E(πs) from Equation 10. Differentiating this

equation when it is evaluated at the optimum in Ωδ , we get:

δδδδ

ππΩ∂

∂−++

Ω∂

∂=

Ω∂∂

=Ω∂

∂ ***

**

)()()( o

ptpops

es q

vcccqcE

(13)

We know that 0*

<Ω∂

∂

δ

pc, so that an increase in uncertainty Ωδ causes the optimum charge by

the supplier to the buyer to fall, the first term in Equation 13. The second term of Equation 13

whose negative sign we established before, 0*

<Ω∂

∂

δ

oq, suggests that the effect of uncertainty

Ωδ on the buyer’s order size is negative, so long as saca

u+−

−+<Ω 2

211 σδ holds, as we discussed

earlier. Thus, we can conclude that Ωδ also adversely affects seller firm’s profits, 0*

<Ω∂

∂

δ

π es

. We

summarize this result as follows:

Proposition #3 (The Uncertainty Reduction-Profitability Link Proposition): The seller firm’s profit level is adversely affected by demand and supply uncertainties and by the unanticipated excess inventory build-up facing the buyer down the supply chain. Thus, a reduction in the demand and supply uncertainties and the excess overstock of the buyer firm will also improve both the buyer and the supplier firm’s profits.

Interpretation

This finding is important for several reasons. It explains the mechanism by which the recent

inventory among large retail firms (e.g., Hewlett-Packard/Compaq, Dell, Best Buy, etc.), led by

the slowdown in consumer spending, reverberates through the supply chain, causing a more

generalized slowdown and a decline in profitability. In addition, combined with the Procurement

13

Cost-Overstock Link Proposition, and the inequality, 0*

<Ω∂

∂

δ

pc, we obtain an explanation for

why firms may be concerned about the consequences of adopting information technologies that

may lead to sharing information. This seems to be what is happening in the food industry.

Nakayama (2000) reports that the buyer’s adoption of collaborative planning, forecasting and

replenishment (CPFR) systems, which employ EDI for inventory coordination, results in tighter

control of the buyer's mark-up capacity by their suppliers. This effectively raises the buyer's

costs. Interestingly, this is exactly what happens in the model we have analyzed. A decline in

unanticipated overstock,Ωδ , due to better knowledge of the market, contributes to the buyer’s

profits in the shortrun, but raises the cost that the supplier charges the buyer, due to the

opportunistic behavior on the part of the supplier. Together these adversely affect the latter’s

profits. By the same token, a better forecast of final demand and the resulting decline in the

value of Ωδ , tend to improve the supplier’s profits. This finding is echoed in the paper by

Seidman and Sundararajan (1998). As a result, the supplier may have an incentive to subsidize

the buyer’s adoption of information sharing technologies and technology platform strategies

(Riggins, Kriebel and Mukhopadhyay, 1994 and 1995; Riggins and Mukhopadhyay, 1999) such

as CPFR and vendor-managed inventory. This is Nakayama’s (2000) observation: sharing

inventory data reduces uncertainties associated with supply, and benefits the buyer and supplier.

Consider the perspectives of the buyer and supplier in other settings. Although they may be

able to gain from information sharing, there are still ways in which they will be in conflict. In

our model, procurement costs play that role. Since sharing information begins with the buyer in

these cases, there may be some reluctance on the part of the buyer to engage in information

sharing, especially if the expected loss from sharing information exceeds the expected gains.

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The question is then to understand the circumstances under which an information sharing

strategy dominates an information withholding strategy in the game between the buyer and the

seller. We next will expand on the initial model to incorporate the buyer’s aversion to the

potentially damaging loss associated with sharing information.

ANALYZING INFORMATION SHARING IN A SEQUENTIAL GAME

Our emphasis now shifts to the analysis of buyer-supplier information sharing optimization

in collaborative planning, forecasting and replenishment (CPFR) systems. We focus on the

buyer's decision to accept or reject making this investment in the context of a sequential game-

theoretic model in extensive form between the supplier and the buyer. (See Figure 1.)

Figure 1. A Sequential Form Game Theory Model for CPFR Information Sharing

Note: Adoption of EDI and CPFR permits the buyer to drive the value of the demand error integral Ωδ to 0, but the operational costs of matching orders to demand remain. Path 1 is the information sharing strategy path, and results in net long-run expected profit for the buyer of Γ1. Path 2 is the information withholding strategy path for the buyer. The ong-run expected profit associated with this decision is Γ2. Along Path 1, the information of the buyer and the supplier are the same. However, along Path 2, the buyer decides to procure without sharing its private information about final demand, with the result that the supplier and the buyer will have asymmetric information.

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A key assumption of our approach is that the output pricing decision has a shorter time

horizon than the decision on IT investment. This permits us to model output the pricing

decisions contemporaneously and the IT adoption decision sequentially. Formal game-theoretic

approaches such as those we employ here have been utilized in other contexts to study strategic

IT adoption by firms (e.g., Dewan, Jing and Seidmann, 2000; Riggins, Kriebel and

Mukhopadhyay, 1994 and 1995, among others).

The difference in the time horizon between the two decisions means that the buyer may act

strategically with respect to it supplier, even as it acts myopically with respect to prices and

quantities. In our model, the buyer observes the dependence of procurement costs, cp, on

unanticipated over-supply, Ωδ . The buyer’s profits arising from this strategic behavior is found

by substituting the supplier’s cost Equation 11 into the buyer’s profit Equation 8:

])([21*

)21)(1(])()*[(

41* 2

212

2

vsacacsacca

b tpu

tpeb +Ω+−−⋅=

Ω−++

Ω+−−−⋅= δ

δδ

δ

σσπ (14)

Strategy Options for the Buyer

This analysis leads to several strategic options for the buyer firm. The most interesting one is

where the buyer firm has the incentive to use information on final demand (e.g., through point-

of-sale data from stores) to raise its own profits, but to withhold information from its supplier to

keep down that part of product's procurement cost, adversely affecting the latter’s profits.

Another option that is available to the supplier is to increase the buyer’s incentive to adopt by

subsidizing the investment costs associated with procurement platform information sharing

solutions. Whether the buyer firm accepts or rejects this offer will depend on the supply chain

environment, including the size of the critical parameters (e.g., firm size, investment cost, etc.)

and the degree of uncertainty in market demand. Even in the absence of the buyer’s adoption of

CPFR, the supplier still may be able to extract information from the buyer based on the latter's

16

periodic order quantities. The subgame perfect equilibria arise from the buyer’s choice of the

most profitable strategy—whether to adopt CPFR and share information, or not—given the

supplier’s response to the strategy.

Assumptions. We assume the buyer gathers consumer and market data by means of POS

scanners. The data do not automatically help to reduce the size of the estimated error in final

demand, σ2δ, and the unanticipated over-supply, Ωδ , unless the retail firm has adopted other

technologies to analyze and interpret the market data. We further assume that the buyer has

adopted IT capabilities that permit effective internal use of shared information, and EDI for

communication with the supplier. The adoption of internal IT capabilities and EDI cause the

buyer’s costs of handling supplies, ct, to decline, and it is able to forecast demand more

effectively, reducing uncertainty. This causes the variance of the demand error forecast,σ2δ , and

the unanticipated over-supply, Ωδ , to fall.

For simplicity, we also will assume that demand-related uncertainty is eliminated, so that the

demand error forecast, σ2δ , and the anticipated over-supply Ωδ will be equal to zero. The drop in

demand uncertainty benefits the buyer as we have seen. This will benefit the supplier, as we

have seen, if the buyer is willing to enter into full-fledged information sharing of market

information and data with the supplier, as with CPFR adoption. Another immediate advantage of

full-fledged information sharing is the reduction in supply uncertainties that arise form supply

chain coordination under CPFR, so that σ2u also goes to zero. Information sharing is beneficial

to the seller in both respects.

Buyer and Supplier Impacts. The buyer faces some trade-offs, however. He benefits from

the reduction in supply and demand uncertainties. But sharing final demand information with

the supplier increases the supplier’s ability to exercise market power over the buyer via product

17

procurement costs, cp. For this reason, the buyer may be reluctant to share this market

information with the seller despite the informational gains of information sharing to both sides.

The evidence suggests that the supplier may be willing to subsidize the buyer in its sharing of

this information, e.g., in the food industry (Nakayama, 2000). Riggins, Kriebel and

Mukhopadhyay (1994), and Seidmann and Sundarajan (1998) model transfer payments of this

type in supply chain management.

The buyer’s decision about whether to accept or reject an offer by the supplier to share

information using CPFR will depend on parameters describing the business environment of the

B2B relationship. If the buyer rejects the supplier’s offer, then the former will continue to rely

on its own internal systems (such as its enterprise system or internal forecasting capabilities), and

not have access to CPFR. Enterprise systems use EDI capabilities for ordering and logistics

between the supplier and buyer. So if the buyer fails to adopt CPFR, but it still has these other

capabilities, then its ability to obtain and share information will be incomplete, and will not

extend to the most sensitive market data.

The Buyer’s Adoption of the Supplier’s Offer of CPFR: Information Sharing

The general expression for the buyer’s profits with respect to its observation of the

dependence of procurement costs, cp, on the unanticipated over-supply Ωδ, was presented in

Equation 14. The buyer’s strategy options are based on evaluating the associated profit stream

under different informational schemes. We will evaluate net long-run profits, by taking into

account the amortized fixed cost of IT. We first analyze the case in which the buyer adopts the

CPFR approach that the supplier offers. With full-fledged information sharing through CPFR,

we are effectively assuming that the supply and demand error variances are eliminated, as shown

by Path 1 in Figure 1. When this is the case, the buyer’s profit function becomes:

18

πbe* | info sharing = 222 )'(

161)',0,0,0(* vca

zcc tttu

eb −−=<=σ=σ=Ωπ δδ (15)

The buyer's net long-run profit, Γ1, from this decision is its equilibrium profit from Equation

15, adjusted downwards for the annualized cost to finance the fixed cost of adoption. If r is the

interest rate, F1 the fixed cost of an enterprise system, and F2 the fixed cost of IT to support

additional internal analysis of the information that the supplier shares with the buyer (e.g.,

category management), the net long-run profit for Path 1 for the buyer is:

)()'(16

121

21 FFrvca

z t +−−−=Γ (16)

The Buyer’s Rejection of the Supplier’s Offer of CPFR: Asymmetric Information

This case, described by Path 2 in Figure 1, is interesting to analyze because it can explain the

observed anomalous behavior in the supply chains. We pointed out earlier that buyers in supply

chain management operations tend to underinvest in IT that promotes information sharing

because they are concerned about such issues as trust and the sharing of benefits. Traditional

retailers have been especially concerned about issues of trust, and especially whether sharing

consumer demand and inventory state information for the purposes of procurement and

replenishment might threaten profitability when potential rivals exploit this private information

for their own gain. In the food industry this issue has been particularly significant. Kinsey and

Ashman (2000) point out that this may be why market leaders that have adopted product bar

codes and scanner technology have lagged behind in the adoption of e-procurement and

information-driven replenishment practices such as CPFR.

We can explain this by recognizing the extent to which information is a strategic asset for the

firm, to be guarded and, at times, even withheld, when circumstances warrant. Consider

19

0)(=

p

s

dcdE π and 0

*<

Ω∂

∂

δ

pc. The unit cost of procurement, cp, rises to the buyer as a result of

smaller values of the demand forecasting error integral, Ωδ, representing a reduction in

unanticipated over-supply. So we see that improved information to the supplier as a result of

CPFR-type information sharing arrangements has the paradoxical potential to raise the buyer’s

costs. Thus, buyers who act strategically with respect to information sharing would observe this

adverse dependence on procurement costs arising due to the information sharing arrangements

with the supplier. Thus, the buyer may find it beneficial to withhold sales information from the

supplier, foregoing the benefits of CPFR in terms of inventory coordination with the supplier, so

that Ωδs will stay the same, and choosing to reject CPFR as a profitable IT strategy.

Therefore, although the supplier remains uncertain about the state of final demand facing the

the buyer, the buyer still can estimate its final demand without undue uncertainty by adopting

other more internally-focused IT approaches (e.g. enterprise systems and category management)

for use with its own POS scanner data. The buyer’s decision to withhold its data as proprietary

information means that it will now be different from the supplier's, leading to an information

asymmetry. The buyer’s profits under this strategy arise from evaluating the maximum expected

value of the buyer’s equilibrium profits in Equation 14. We take special care to distinguish the

information uncertainty experienced by the buyer, Ωδr and σδ

r2, from that of the supplier, Ωδs and

σδs2. In the maximization of the buyer’s expected profits in Equation 8, the buyer’s own

information effect enters directly, but the information effects from the wholesaler operate only

via the unit cost parameter, cp*. To be consistent with our presentation of the full-fledged

information sharing case, we present the buyer’s expected profit function for the no information

sharing case in a similar manner based on Equation 14:

20

πbe* | no info sharing =

',0,0,2

)(*)21)(1(4

])()*[( 22

212

2

ttrr

st

prru

rtp ccvsacac

z

sacca<==Ω

+Ω+−−=

Ω−++

Ω+−−−δδ

δ

δδ

δσ

σσ (17)

The supplier perceives a demand error integral value, Ωδs, for anticipated over-supply. The

reader should also notice that similar to the information sharing strategy, the internal transaction

costs to the buyer, c’t, are less due to its internal IT investments. The supplier is aware of this

lower transaction cost and uses c’t to evaluate ct, which appears as c p* in Equation 17, the

procurement cost expression, and also directly in the profit term. The amortized fixed costs of

the related IT are the same as in the information sharing strategy. Evaluating Equation 17, the

net long-run profit from adopting an asymmetric information strategy, Γ2, is:

)()1(16

])()'[(212

2

2 FFrb

savca

u

st +−

+

Ω++−−=Γ

σδ (18)

So, it appears that the net long-run expected profit for the buyer Γ2 rises with Ωδs.

Proposition 4 (The Buyer’s Information Withholding Proposition): The effect of a buyer withholding proprietary market information from its supplier is to increase the buyer’s profits, all else equal.

Compared to the information sharing strategy payoff in Equation 15, the price paid for the

buyer's refusal to share information is the supply uncertainty and poor procurement coordination,

represented by σu2. We next discuss the equilibrium value of Ωδ

s and examine this trade-off.

EQUILIBRIUM ANALYSIS FOR THE ASYMMETRIC INFORMATION STRATEGY

Before we can examine what the outcome of this game will be for the supplier and the buyer,

the nature of the information that they possess must be more closely examined. In this section,

we discuss what determines the equilibrium value of the demand error integral for the supplier,

Ωδs, and further examine what is involved in the analysis of the trade-offs.

21

Revealed Equilibrium Signal with Asymmetric Information: Case of Multiple Equilibria

The key aspect of the asymmetric information exchange between the buyer and the supplier

turns out to be that despite the buyer's withholding of sensitive final demand data from the

supplier, the latter will is still able to extract some valuable information from the buyer. This

occurs because the exchange is based on orders arriving from the buyer that must be filled by the

supplier. To see this, we begin by noting that market equilibrium between the buyer and the

supplier arises if an expectation realization condition is satisfied: namely, that the expected

quantity of orders forecasted by the supplier matches the certainty equivalence level of orders by

the buyer. This equality comes from applying the expression for the optimal order quantity,

)21)(1()()(

21* 2

212

δδ

δ

Ω−σ+σ+Ω+−−

⋅=u

osaca

zq , to yield the following:

qs* | order quantity expected by supplier = qb

* | order quantity received from buyer

)21)(1(

)()('(21

)21)(1(

)()('(21

22122

212 bb

u

bspt

ssu

sspt sacca

zsacca

zδδ

δδ

δδ

δδ

σσσσ Ω−++

Ω+−Ω−−⋅=

Ω−++

Ω+−Ω−−⋅ (19)

The unit cost, c, in the expression for q0*, consists of a transaction cost component and a

procurement cost component, and depends on the demand-related error integral, Ωδs, as in

Equation 17. The superscript s is the uncertainty as seen from the perspective of the supplier.

Yet, in fact, cp(Ωδs) shows up to both parties in the same way. Why? On the one hand, the

supplier has access only to information it perceives. On the other hand, the buyer knows this to

be the case for the supplier. So this suggests that although the supplier acted strategically in

terms of supply quantity, the buyer is able to act strategically with respect to the signals that are

present in the game. Beyond that, however, the buyer operates on the basis of its own

information, Ω bδ and (σ bδ) 2. Finally, we assume that the buyer has access to full information

22

about the market in which final consumer demand is established (which it withholds from the

supplier), so that Ω rδ = (σ δr)2 = 0, while Ωδs = (σδ

s)2 = 0. The demand error integral, Ωδs = 0,

allows for the possibility that the supplier’s knowledge of the market facing the buyer through

the procurement process is complete. Equation 19 has two roots, one of which corresponds to

complete information. These are and 0)( 1* =Ω δ

s

savca ts

+−−

−−

=Ω'

22)2

*

αδ

δδδ )( df δσ δ ∫−

≡1

1

2

( , respectively, where α

is a constant less than 1. The parameter α is characteristic of the underlying density function.

We assumed that 1/2(σ sδ) 2 = α Ωsδ, with α < 1, to eliminate (σ sδ)2 in favor of Ωs

δ. This

assumption is based on the definitions of , and , and the fact

that δ

δΩ ∫≡1

0

δδ2 )( df

2 < δ <1. Figure 2 depicts the quantity curves for the two-sided certainty equivalent in

Equation 19, as well as their intersection associated with the two solutions.

Figure 2. Determination of Information Equilibrium in Supply Chains q

os *

23

With an increase in informational asymmetry Ωs

δ due to information that is withheld from

the supplier but is available to the buyer, the quantity ordered by the buyer rises, but the quantity

expected by the supplier falls, though with a discontinuity at 1/(2-α). (There is also a case in

which q0* | order quantity expected by supplier rises with Ωδ

s. However, we rule this case out since it leads

to the result that sa

vca t

+−−

<−'

2 α . This is impossible since 2-α > 1, while 1'

<+

−−sa

vca t .) For the

supplier’s expected quantity to fall in Ω sδ we must have 1/(2-α) > (a - co’ – v) / (a+s). This

guarantees that the second root of Equation 19 is positive, i.e., (Ω sδ*)2 > 0. But it also

guarantees that (Ω sδ*)2 > 1/(2-α).

Thus, the discontinuity separates the two equilibria, i.e., we have a case of separating

multiple equilibria. Since the solutions are separated by this discontinuity, it follows that the

initial level of informational asymmetry determines which equilibrium value of Ω sδ is reached.

This is an instance of what we have referred to as a path dependency.

Information Convergence and Separating Equilibria

Our model is an example of a class of models in Economics that are known as signaling

models (e.g., Spence, 1973, who discusses job market signaling via educational levels). Buyers

have the capability to signal the expected state of final consumer demand through the orders that

they place up the supply chain. Suppose the buyer begins with an initial level of market

uncertainty corresponding to the mean unanticipated over-supply of Ω oδ.. As the buyer reveals

information about the market to the supplier, the level of uncertainty perceived by the supplier

Ω sδ will gradually decline from its original level of Ω oδ,. But where does the final equilibrium

solution occur? The answer depends on the relative size of Ω oδ compared to the discontinuity

point of (Ω sδ)Discontinuty = 1/(2-α). We distinguish among three scenarios:

24

Scenario A (Low Market Uncertainty). Initial market uncertainty is very small such

that (Ω sδ*)1 = 0 < Ω oδ < 1/(2-α) < (Ωs

δ*)2. In this case, (Ωs

δ*)1 = 0 will be binding and

the supplier’s inference will lead to full information convergence.

Scenario B (Intermediate Market Uncertainty). Initial market uncertainty is of

intermediate size such that (Ω sδ*)1 = 0 < 1/(2-α) < Ω oδ < (Ω sδ

*)2 . If this is true, then

1/(2-α) will be binding and the supplier’s inference leads to information convergence.

Scenario C (High Market Uncertainty). Initial market uncertainty is large such that

(Ω sδ*)1 = 0 < 1/(2-α) < (Ω sδ

*)2 < Ω oδ.. In this setting, (Ω sδ*)2 will be binding and the

supplier’s inference converges to this point.

Note that because of the underlying discontinuity in supplier profits in Figure 2, the

convergence of information will be towards either (Ω sδ*)1 or (Ω sδ

*)2 (depending on the position

of Ωδo ) but not both. We summarize these results in the following proposition.

Proposition 5 (The Inferred Equilibrium Proposition). If market uncertainty is low, then supplier inference from the buyer’s orders leads to an equilibrium with full infor-mation (Ω s*

δ)1 = 0 (Scenario A). If market uncertainty is moderate then supplier infer-ence leads to an equilibrium so some uncertainty facing the supplier still remains and is equal to 1(1-α) (Scenario B). If market uncertainty is higher, then supplier inference leads to an equilibrium with greater residual uncertainty equal to (Ω s*

δ)2 (Scenario B) .

These results suggest that high information asymmetry cannot be rectified in a market with a

high degree of uncertainty, but it can be when the uncertainty is less. Overall, information

withholding strategies are more harmful in markets with high levels of uncertainty than limited

uncertainty. This may be why information sharing is greater when market variance is greater

(e.g., electronics, airlines, travel) than when it is lesser (e.g., food, construction supplies).

Strategy Dominance and Information Convergence

When should the buyer switch strategy? We consider the profit streams of the buyer under

the information sharing strategy and the information withholding strategy. (See Figure 3.)

25

Figure 3. Information Sharing and Information Withholding Strategies

Γ

Γ2(Ωδs)

Γ1

Case C1: Ω oδ >ΩTδ >(Ωs

δ*)2 .

Partial information convergence to (Ω sδ

*)2. Information.is initially withheld but sharing dominates in equilibrium.

Γ

Γ2(Ωδs)

Γ1

Γ

Ωδ

Ωδo

Γ2(Ωδs)

Γ1

2

α−21

(Ωsδ)*

2

Ωδo

Γ

Γ2(Ωδs)

Γ1

0Ωδ

α−21

Γ

Γ1.2(Ωδs)

Γ1.1

Ωδo

Ωδ

α−21

Γ2 (Ωoδ)< Γ1 Γ2 (Ωo

δ)< Γ1

Case C2: Ωoδ > (Ωs

δ*)2 >ΩT

δ.. Partial information convergence to (Ω sδ

*)2. Information withholding dominates initially and in equilibrium.

Ωδ

Ωδ

(Ωsδ)*

1=0

1 Ωδ

o Ωδo ΩT

δ

α−2

(Ωsδ)*

2

(Ωs

δ)*1=0

1 2ΩTδ

(Ωsδ)*

(Ωsδ)*

1=0

ΩTδ

Cases A1 and A2: Ωoδ < Ω Tδ .

Then Γ2 (Ωoδ)< Γ1 and information

sharing always dominates.

(Ωsδ)*

1=

α−2

ΩTδ

(Ωsδ)*

(Ωsδ)*

1=0

(Ωsδ)*

2

ΩT

δ

Case B: 1/(2-α)>Ω oδ >ΩTδ . Full

information convergence. Information is initially withheld but dominates in equilibrium.

26

We view both as a function of uncertainty, and use them to characterize when a switching

strategy is appropriate. Under the information sharing strategy this demand-based uncertainty is

eliminated so that the net long-run expected profit for the buyer, Γ1, becomes a flat line,

corresponding to Equation 15. However, under the information withholding strategy, when the

buyer has access to information but does not share that with the supplier, the buyer’s profits, Γ1,

increase with market uncertainty, as suggested by Equation 16. The two profit functions

intersect at a point on the demand error integral axis—say Ω Tδ —that defines the threshold value

of market uncertainty for switching IT strategies, as follows:

sa

vca ouT

+−−−+

=]][1]1[ '2/12σ

δΩ (20)

When we compare Ω Tδ with the second root (Ω sδ*)2 solution to the certainty equivalence

expression in Equation 19, we find that, depending on (a) the positions of two information

parameters, i.e., the initial market uncertainty Ω oδ and the switching uncertainty Ω Tδ,, and (b)

the initial profit advantage of the information withholding strategy, three outcomes are possible:

that strategic value of the information withholding vanishes, is actually reversed, or its relative

margin diminishes but it remains dominant. We distinguish three scenarios:

Scenario A (Low Market Uncertainty): Ω oδ < Ω Tδ . Then Γ2 (Ω oδ) < Γ1 . In this case

an information sharing strategy always dominates. (See Figure 3, Cases A1 and A2.)

Scenario B (Intermediate Market Uncertainty): 1/(2-α) > Ω oδ > ΩTδ: In this case,

information is initially withheld but the information withholding “rent” dissipates in the long

run, due to information leakage to the supplier. There is full information convergence.

(See Figure 3, Case B).

27

Scenario C (High Market Uncertainty): Ωoδ > max[Ω Tδ , (Ω sδ

*)2 ] > 1/(2-α). Then Γ2

(Ωoδ) > Γ1. Case C1 is similar to Case B in that an information withholding strategy

dominates initially but the information withholding “rent” dissipates in the long run and

in fact reverses, due to information leakage to the supplier. However, unlike Case B,

information convergence is partial. In Case C2, the information rent is can be sustained

maintained even in the long-run. (See Figure 3, Cases C1 and C2.)

Cases B and C1 are particularly interesting. Here, the buyer withholds information from the

supplier, yielding greater initial profits. However, due to the supplier’s learning and inference,

information convergence leads to a new equilibrium profit that is so much lower as to make an

information withholding strategy inferior to the outcome for the firm if it had implemented an

information sharing strategy to begin with. This path dependence arises because the firm’s

benefits of information sharing strategy are no longer available while the benefits of information

withholding strategy vanish due to learning and inference by vendor firm. To summarize:

Proposition 6 (The Buyer’s Feasible Strategy Proposition). Information sharing or withholding strategies may both be feasible strategies for the buyer. However, in some circumstances a buyer’s information withholding strategy locks him into a path-dependent lower long-run profit, due to information leakage to the supplier.

CONCLUSION

The emergence of supply chain strategies and technologies has contributed to the cost

reductions and increased procurement coordination that we have observed over the past few

years across many industries. Yet, the continued expansion of supply chain practices depends in

large measure on firms’ willingness to share what they view as sensitive information about

demand, operating costs, and their customer relationships. How likely is the continued adoption

28

of IT-based supply chain practices, in the light of firms’ efforts to achieve an appropriate balance

between profit-maximizing sharing or withholding of inventory and sales information?

We explored this question using a sequential game-theoretic framework that emphasizes the

central role of buyer uncertainty with respect to final consumer demand in a retailing supply

chain setting. We found circumstances where both information sharing and information

withholding might take place depending on the degree of initial uncertainty about market

demand. But our most interesting result involves the recognition that a buyer that finds

information withholding to be efficient initially may find itself locked into an less efficient

outcome in the long run, as the upstream firms along the supply chain are able to infer the

downstream firm’s sensitive information. This signaling mechanism becomes operative through

orders that a buyer places with the supplier. It permits the supplier to infer information about

final demand that the buyer is likely to face, permitting the supplier to potentially engage in

profit-maximizing strategic behavior. Our results are consistent with some of the findings in

prior research (especially Radharkrishnan and Srinidhi, 2003, and Cachon and Fisher, 2000), and

retains the general theoretical perspective that information sharing will only be implemented by

supply chain partner when the buyer and supplier are no worse off by exchanging information.

We also developed a basis for why the observed information sharing regime selections may

be path-dependent. Our interpretation of how the buyer’s decision about which regime to adopt

comes about is predicated on the idea that adoption is not forced (Cachon and Lariviere, 2001)

and that information is shared without player dishonesty or inaccuracies (Brown, 1999). Thus,

by withholding all shared information except procurement orders, the supplier is truly unable to

know more than the buyer’s ordering signals communicate about consumer demand.

29

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